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Rewrite the following equation as a function of [tex]\(x\)[/tex]:

[tex]\[
\frac{1}{16} x + \frac{1}{320} y - 29 = 0
\][/tex]

A. [tex]\( f(x) = -9,280 + \frac{1}{16} x \)[/tex]
B. [tex]\( f(x) = 9,280 - 20 x \)[/tex]
C. [tex]\( f(x) = -9,280 + 20 x \)[/tex]
D. [tex]\( f(x) = 9,280 - \frac{1}{16} x \)[/tex]



Answer :

GinnyAnswer
To rewrite the equation [tex]\(\frac{1}{16} x + \frac{1}{320} y - 29 = 0\)[/tex] as a function of [tex]\(x\)[/tex], follow these steps:

1. Isolate the term containing [tex]\(y\)[/tex]: First, let's isolate [tex]\(\frac{1}{320} y\)[/tex] by moving the other terms to the right side of the equation.

[tex]\[ \frac{1}{320} y = -\frac{1}{16} x + 29 \][/tex]

2. Eliminate the fraction involving [tex]\(y\)[/tex]: To eliminate the fraction [tex]\(\frac{1}{320}\)[/tex], multiply both sides of the equation by 320.

[tex]\[ y = 320 \left( -\frac{1}{16} x + 29 \right) \][/tex]

3. Distribute the constant 320 to both terms inside the parentheses:

[tex]\[ y = 320 \cdot -\frac{1}{16} x + 320 \cdot 29 \][/tex]

4. Simplify the terms:

[tex]\[ y = -20x + 9280 \][/tex]

5. Rewrite as a function of [tex]\(x\)[/tex]: Let's express [tex]\(y\)[/tex] as [tex]\(f(x)\)[/tex].

[tex]\[ f(x) = -20x + 9280 \][/tex]

Now we compare our result to the given options:

A. [tex]\(f(x) = -9,280 + \frac{1}{16} x\)[/tex]

B. [tex]\(f(x) = 9,280 - 20 x \)[/tex]

C. [tex]\(f(x) = -9,280 + 20 x\)[/tex]

D. [tex]\(f(x) = 9,280 - \frac{1}{16} x\)[/tex]

The correct option that matches our result, [tex]\(f(x) = -20x + 9280\)[/tex], is:

B. [tex]\(f(x) = 9,280 - 20 x\)[/tex]

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